New Criticism is a formalist literary criticism in which critics approach the work of literature as a stand alone work, as if it were self-contained. The reader's response, author's intention, or historical and cultural contexts are not considered as important as the inherent qualities of the work. New Critics believe the structure and meaning of the work of literature should not be examined separately. They pay special attention to the use of literary devices in a text. So, if you want to criticize Young Goodman Brown as a New Critic, in the strictest sense of the word, you would have to ignore its historicity. That is hard, don't you think? Because part of the impact of this short story is the historical context in which it was written and the society and values it was meant to criticize, the Puritans.

But, let's be New Critics and look at the work itself, irrespective of its historical milieu. The work can be viewed as an allegory for hypocrisy. This is certainly a modern idea and can be appreciated in this work whether it is criticizing Puritan society or 21st century society. Does the short story create an effective allegory in your mind? What about the symbolism? There are some very strong symbols in this story that a New Critic would appreciate, especially as they relate to the theme of hypocrisy. There are the wife's pink hair ribbons, the stick that turns into a snake, the trees of moral support the preacher attempts to cling to amidst his wavering faith. Also, take a look at the foreshadowing. It is excellent. The dark forest, the darkness of the Minister's soul, the description of the devil. Look at the metaphors, personification, similes and imagery in the text:

He had taken a dreary road, darkened by all the gloomiest trees of the forest, which barely stood aside to let the narrow path creep through, and closed immediately behind.

Hawthorne is very skilled at creating mood with words.

You can read about this short story as well as read the text of it right here on eNotes.